KCET · Physics · Nuclear Physics
A nucleus \({ }_{Z} X^{A}\) emits an \(\alpha\)-particle with velocity \(v\). The recoil speed of the daughter nucleus is
- A \(\frac{A-4}{4 v}\)
- B \(\frac{4 v}{A-4}\)
- C \(v\)
- D \(\frac{v}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{4 v}{A-4}\)
Step-by-step Solution
Detailed explanation
Let the recoil speed of daughter nucleus is \(v^{\prime}\).
By the law of conservation of momentum, we have
\(0=(A-4) v^{\prime}+4 v\)
or
\(\begin{aligned}
(A-4) v^{\prime} &=-4 v \\
v^{\prime} &=-\frac{4 v}{(A-4)}
\end{aligned}\)
By the law of conservation of momentum, we have
\(0=(A-4) v^{\prime}+4 v\)
or
\(\begin{aligned}
(A-4) v^{\prime} &=-4 v \\
v^{\prime} &=-\frac{4 v}{(A-4)}
\end{aligned}\)
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